Invariant object recognition

ABSTRACT

A system and method of identifying the computing architecture used by the mammalian visual system and to implement it in simulations and software algorithms, and in hardware components, is described.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.11/035,412, which was filed Jan. 14, 2005, now allowed, which claimspriority to U.S. Provisional Application No. 60/536,261, which was filedJan. 14, 2004, and is titled “INVARIANT OBJECT RECOGNITION,” all ofwhich are incorporated by reference.

TECHNICAL FIELD

This description relates to invariant object recognition.

BACKGROUND

Object recognition is a cornerstone of the function of visual systems,whether neural or manmade. This capacity is indispensable for thefunction of a sensorimotor system operating in an external world,whether for navigation in complex terrain or rapid identification of theproperties of food, friend, or foe. However, developing a manmade systemto perform object recognition, which is so immediate and effortless forneural systems such as the mammalian brain, has proven toweringlydifficult for conventional computing systems and software, despitedecades of effort in computer vision and related fields of engineering.The best manmade systems for object recognition labor to deal withchanges in the orientation and scale, and are defeated by the occlusionof one object with others which ubiquitously occurs in environments.Such performance is intolerable in any real-world application, whethermilitary or commercial.

SUMMARY

In contrast to the limited performance of extant engineering algorithmsand related hardware for this indispensable problem, all neural systemsendowed with vision accomplish object recognition nearly immediately onthe timescale of their circuitry, and accomplish the task in the face ofreal-world conditions where occlusion is common, and with radicalchanges in scale as for example occur when a predator approaches itsprey. The difficulty encountered in attempting to solve this problemwith conventional engineering, mathematical and computer science methodshints that conventional algorithms and computing architectures are notsuited to this problem. In contrast, the performance of neuralarchitecture in accomplishing real-world object recognition speaks foritself.

What then is the neural architecture which is responsible for the powerof object recognition in the brains of animals? We know its performancemust be such that object identification can readily occur despitechanges in the scale of the image, its lighting, occlusion, rotation,position in the visual field, and other such transformations of theimage which occur in the ordinary course in the natural world.

Natural visual systems take in raw sensory data, which typically shiftsas an object moves across the visual sensory array (the retina), andtransform it into an invariant representation associated with theidentity of the object, enabling a fast decision to be made aboutappropriate reaction. Thus, fast neural visual object recognitionrequires the sequence of patterns representing an object on the retinato be transformed into a stable pattern uniquely encoding the objectitself. The desired system therefore is a self-organizingcontent-addressable memory: the retinal image or low level preprocessorencoding triggers the activation of a high level object representation.Iterative computation is not required.

We know that the mammalian cortex includes primary areas which receivedirect thalamic input, where the pattern on the visual sensor surface ofan apple is entirely different depending upon whether it is close to orfar from a monkey. Nevertheless the pattern of activity triggered in thehigher association areas, particularly in the inferotemporal cortex, isquite invariant to the scale of the object (Tanaka et al 1991). Further,this higher visual area has been shown by selective lesion studies(Mishkin 1981) to be vital for successful object recognition inprimates, suggesting that the invariant encoding in IT cortex isrequired for the behavioral performance display of object recognitionfunction.

Conversely, though an apple and a rock of similar size and shape triggerhighly overlapping initial images on visual sensors (the retina), thesetwo objects nevertheless trigger different patterns in the highercortical areas which have been shown indispensable for objectrecognition. We conclude that powerful neural sensory systems for objectrecognition must be capable of solving the following paradox: theoverlapping representation of different objects of similar size,location and shape must trigger activation of different representationsin higher areas, while the entirely non-overlapping and dissimilar earlysensory patterns triggered by the same object in different positions inthe external world must trigger an invariant pattern in some deeper areaof the neural system, encoding the presence in the environment of thegiven object regardless of its position, orientation or closeness ofapproach. We seek here to identify the neural mechanism for invariantobject recognition in mammals, and to quantify its computationalperformance advantage (in the sense of timesteps required to produce theinvariant representation given the initial sensory surface activation)over conventional computing hardware and algorithms. Some grasp of theextraordinary power of the neural systems for object recognition may begained by recognizing that in mammalian systems, which use neuralcomponents operating at frequencies less than 250 Hz, 150 millisecondsis adequate for object recognition to occur in complex real-worldenvironments. We seek therefore to identify the computing architectureused by the mammalian visual system and to implement it, first insimulations and software algorithms, thereafter in hardware components.

The details of one or more embodiments are set forth in the accompanyingdrawings and the description below. Other features and advantages willbe apparent from the description and from the claims.

DESCRIPTION OF DRAWINGS

FIGS. 1-5 are block diagrams illustrating visual representation ofobjects invariant to transformation.

DETAILED DESCRIPTION

What military and commercial value might reside in circuitry which couldaccomplish the identification of a moving visual object within a smallnumber of timesteps? The range of the applications are enormous. Amissile tracking system needs to discriminate a target from all mannerof noise and distractors. A robotic vehicle exploring a hostile ordistant environment needs to navigate in close quarters in a terrainfilled with objects, identifying and characterizing the properties ofboth targets and obstacles. Autonomous commercial vehicle navigationsystem can require the ability to distinguish the identity of movingobjects. An artificial visual system aiding the blind requires theability to identify nearby objects. The classic legacy commercialapplications range from face recognizition to character recognition forhandwritten characters, in all languages. More distantly, anyintelligent robot with visual sensory function can presumably navigatean environment populated with objects which must be identified for therobot to function adequately. Object recognition has been a central goalof computer vision research for decades, because it is a cornerstone ofvisual function, with application to all intelligent devices whichemploy visual sensors.

In one aspect, a demonstration simulation of the architecture proposedcan be engineered to solve the invariant object identification problem,working on large set of simple objects moving through a virtual visualenvironment. A basic approach can be modeled after Rhodes 1992, which isincorporated by reference in its entirety. As further detailed below,the architecture proposed is based upon the circuit elements, wiringarchitecture, and connection (synaptic) properties of the mammaliancortical hierarchy, a neural structure which accomplishes objectrecognition in real-world environments rapidly, and which encodesrepresentations of visual objects which are invariant with respect tochanges in object size, orientation, and position in the visual field.The system functions as a self-organizing content-addressable memory, inthat simply feeding in the visual images causes a cascade of feedforwardinputs which result in increasingly invariant representations of theobject presented to the system with each succeeding “cortical” area. Theinformation is stored in the wiring connectivity itself, which is builtup as the system is exposed to the objects moving through the visualfield, as during normal experience.

In another aspect, the computation power of the proposed neuralarchitecture to perform object recognition can be quantified andcompared to conventional methods. When the algorithm is working insoftware on simulated 2-d images, the computation floating point loadrequired to solve the problem using the proposed neural architecture canbe directly calculated. The floating point operations required forconventional algorithms developed for invariant object recognition canbe estimated and compared. Finally, the speed of the neural architecturewhen implemented in VLSI can be estimated, to assess the utility of thisarchitecture for real-world problems.

Other important features can include the architecture of a hierarchy ofcortical areas, the properties of the synaptic connections, particularlythe temporal integration across images afforded by the NMDA receptorproperties embodied in cortical excitatory synapses, local interneurons,integration of the feedforward synaptic input in the electrically activebranches of dendritic trees, development of a virtual environment and aclass of visual objects which can move within that environment, allowingfor dilation (as when an object is approached) rotation, andtranslation, testing of the system performance, and quantification ofthe number of timesteps required for completion.

Most conventional computer vision algorithms for invariant objectrecognition use a highly computationally intensive three-part strategy:first, the presence of an object is identified, with some form offigure-ground segregation methods; second, the object is transformedinto a centered and normalized reference frame (object-centeredcoordinates) so that it may be compared with stored exemplars; thecentered and normalized object is then matched to a template, or a setof related templates (e.g. Würtz 1997), or compared with objecttemplates using basis-function or principal component methods. In thesesystems, not only is there computational load in the figure-ground andnormalization procedures, but then all the stored objects must beiteratively compared with the normalized object of interest. Thecomputational load of this strategy has made it very much unsuited forreal-time applications. It bears no relation to biologically plausiblecomputational operations. Because of the evident power of biologicalvisual systems in performing object recognition, one seeks more neuralarchitectures.

A variety of neural network architectures can be suitable for thesystems. Starting with the Neocognitron of Fukushima (1980), there hasbeen a 20 year long tradition of neural network architectures devised toaddress invariant object encoding, many using some hierarchy ofprocessing layers. In Fukushima's work, feature filter layers arefollowed by pooling layers, where translational invariance of featuresensitivity across some translation distance is accomplished by wiring aset of position-dependent feature filters of the same orientation but atdiffering locations across space to the same unit in layer 2, with thisprocess iterated. More sophisticated versions of this class of systemhave been developed (Wersing and Körner 2003), in which the connectivitymatrixes are determined by gradient descent in the inner product betweenfeature detectors and image patches, with some form of competitionenforced at each layer. Thus the weights do not self-organize in thisclass of algorithms. The solutions in the literature offer manyattractive means to construct first order feature detectors whichdecompose natural images (an elegant example is in Olshausen and Field1997), generally resulting in collections of edge-sensitive detectors,but the subsequent step of constructing higher order features (i.e.features which represent sets of primitive features) is less elegantlysolved, for example with explicit principal component analysis (for arecent example Wersing and Körner 2003) to determine the most usefulintermediate order feature for classifying a given training set. This isan offline, normeural, and computationally expensive method.

In one well-known solution to optical character recognition (Lecun etal. 1998), which has features of a highly constrained invariant objectencoding problem, the best early-stage as well as intermediate-stagefeatures are determined by error backpropagation, where the choice ofwhich combinations of feature primitive are combined to makeintermediate stages (higher order) features is explicitly determined bysupervised gradient descent to minimize classification errors on atraining set. However, backpropagation is implemented with a highlynon-neural architecture, which is known to scale very poorly in highdimension problems (i.e., in environments with complex images andcontexts), and so while tractable for character recognition is notsuitable for real-world problems. What is needed, are self-organizingalgorithms, where the weights between neurons develop themselves duringexperience based upon local synapse-modification rules, and one which isnot defeated by the complexity scale-up inherent in real-world problems.The intermediate layers, which encode higher order features, shouldthemselves self-organize, with local rules, which can be iterated in ahierarchy of layers. And the encoding should be distributed, so that apattern of activation across a 2-dimensional cortical sheet encodes thepresence of an object, for the benefits of distributed representations(fault-tolerant, graceful degradation, generalization to unfamiliarobjects). Again, biological neural systems (as differentiated fromneural network systems) inherently self-organize, and do scale up tohandle real-world complexity; we are led to advocate emulation of theneural circuitry and local cellular and synaptic which has evolved inbiological systems to solve these problems.

Dynamic link architecture can be a more neural approach to invariantobject recognition, which relies on a hypothesized property ofconnections between neurons.

In biological neural object recognition, there is no supervisedlearning, all computations are local in space and in time. Further, andcritically, biological creatures do not (and for survival cannot)process and reprocess over many computation cycles in order to settle onthe identification of an object in their environment. A predator must beidentified immediately and appropriate action taken to ensure survival.In the mammalian brain, visual sensory information flows from retinaforward to the thalamus, and thence to a series of visual cortical areasin the following sequence: V1→V2→V4→IT. The pattern of activity in thefirst visual cortical area is transformed in the second, andretransformed, and by the inferotemporal cortical area (IT) (the 6^(th)station of the sequence of areas starting with retina) an invariantobject representation is produced. Importantly, in addition to thefeedforward flow, there is contant feedback from each higher area backto the preceding area, and the feedback is constant and integral to thecircuitry. In mammals, from the time an object appears in the visualfield to the time it triggers an invariant representation is about 150msec (Ungerleider et al. 1994), with much of this time consumed inpropagation delay along axons, and integration time for input to triggeroutput at each neuron in the cascade.

In the neural process achieved in biological system just described, theappearance of an object in the visual field triggers the activation ofthe representation of that object in each area, with the representationincreasingly invariant (to scale, rotation, translation and othertransformations) with each succeeding step up the hierarchy. In thissense, it can be described as a content-addressable memory. The image ofan object, in any position and size, as it passes through a cascade ofcortical areas, triggers activation of a distributed pattern of activitywhich encodes the presence of the object.

Advantageously, biological neural architecture can be implemented ininvariant object recognition hardware. The object recognitionarchitecture of the mammalian cortex can be implemented to use neuronalelements with the local nonlinear integrative properties of corticalneurons. The end goal is a module of synthetic neural circuitry renderedin VLSI which can take in visual (or other sensory) raw data afterprocessing through a topographically organized feature detector, andafter a period of unsupervised learning by presentation of commonobjects moving through the environment, can adjust its connectionstrengths so that, upon later presentation of a familiar object, adistributed pattern invariantly encoding that object shall be activatedin a high-order area.

In this system, the primary flow of information is feedforward, as fromretina to thalamus to V1 and onward into the cortical hierarchy ofareas. Though in the mammalian system there is continuous feedback ateach stage, a ubiquitous aspect of cortical circuitry, the objectcategorization is made within 150 msec, about 85 msec after activityreaches the thalamus, leaving only 20-25 msec for each stage from V1 toV2 to V4 to IT. Given that the feedforward integration and transmissiontime from area to area is about 15 msec, this system largely functionsin a single feedforward pass; thus the object triggers the outputresult, as a content addressable memory. There is no separatefigure-ground operation to identify an object, and no geometrictransformation in order to reach a normalized and centered coordinatesystem, the Achilles heel of conventional methods. The feedforwardconnections in a cascade of several identical processing areas, as withthe hierarchy present in mammalian sensory cortices (Pandya and Yeterian1985) are self-organized during the course of early experience. Thewiring is established not by some supervised method, but rather byexposure to the environment itself.

There are two critical elements to the neural circuitry, which are notfeatures of existing models, which confer great power to the system.They both concern the biophysicals of signal transmission andintegration in cortical pyramidal neurons.

Synaptic connections are strengthened using a temporal eligibilitytrace, so that a synapse which was active a short while ago remainsready to strengthen upon firing of the dendritic branch receivingsynaptic input. In this way, separate features active during temporallyadjacent views of an object become wired to the same cell (indeed to thesame dendritic branch) in the higher area to which they project. Asfirst suggested by Földiák (1991), such a temporal trace in afeedforward area-to-area architecture enables invariant objectrepresentations to form, by linking together succeeding views of anobject as they occur during experience. For example, the NMDA receptorwhich in part mediates biological synaptic transmission has therequisite properties to implement a temporal trace.

In prior work on neural network object recognition, neuronal elementssum input in a simple manner, with linear summation of inputs passedthrough a thresholding function, a classic neural network unit, such as,for example, nonlinear integration of inputs in the dendritic tree ofpyramidal cells. See, for example, Rhodes 1999. It has been predictedthat neuronal input to a branch can fire that branch when the inputexceeds a threshold, so that each branch acts as a quasi-isolatednonlinear element. This predicted phenomenon has recently beenexperimentally confirmed. See, for example, Schiller et al. 2003. Thereconception of neurons as branched structures with nonlinear activeprocesses in each branch greatly enhances the power of neurons ascomputational units, a feature which heretofore has not beenincorporated into neural network research (but see Mel and Fiser 2000)and which can add great power to a new class of neural architectures.This complex power of individual neuronal units can be integral to theability of the proposed system to separate the identity ofsimilar-appearing but distinct objects (i.e., of linearly inseparableobjects) and thus is vital for real-world applications.

FIG. 1 illustrates encoding of the visual world in the primary area. Inparticular, FIG. 1 shows a simplified representation of a processingarea (analogous to an area of the cerebral cortex) which encodes theform of a shape (in this case, a triangle). The complex shape is reducedto a set of edges, each of which is in a different location and has itsown orientation. At “Time 1,” the so called V1 (visual area 1) encodingtakes the retinal image of a triangle, and recodes it into thiscompressed representation. As shown, a moment later, at “Time 2”, thetriangle gets bigger (i.e., as an observing agent approaches the object)and the units encoding the triangle in V1 now change. There is nooverlap between the V1 encoding of the triangle at time 1 with that attime 2, even though it is the same object.

FIG. 2 illustrates encoding of visual world in a higher visual area. Inthe brains of mammals, the representation of an object in higherprocessing areas becomes less dependent upon its position and scale, andmore associated with the identity of the object itself. Thus, in thehigher visual encoding area, the encoding stays invariant as an objectapproaches. This results in a useable representation of the identity andpresence of an object.

The question posed by FIGS. 1 and 2 is how does the wiring to supportsuch an invariant representation arise given that its inputs (here thesignals coming from the V1 array) shift from moment to moment? FIG. 3serves to illustrate the proposed solution to this problem. Theillustration is further simplified to a single row of cells from thevisual primary area and a second row of cells from the visual higherarea where the invariant encoding will be. Here, at Time 1, a singlecell in the primary sensory area is active (representing a single edgeof the triangle in FIG. 1 above). The output wires (axons) of this cellprovide input at a variety of branches (they are called “dendrites” inthe context of biological neurons) of the cells of the higher sensorybank. We will focus on their input to the branch highlighted with thegray circle.

In FIG. 4, at time 2, the object has shifted, and hence the cell activein the primary visual sensory area has shifted. Its output wirestransmit to a variety of branches in the higher area, and there is onesuch branch in common with the recipients of the output of the cellactive at time 1. This second input to the common recipient branch firesthe branch, strengthening that input by a Hebbian algorithm, simply wheninput and target both fire. The properties of the signal transmission inthe proposed system allow the input which was active at time 1, a shorttime before, to also remain ready to strengthen triggered by the firingof the branch.

FIG. 5 illustrates a blowup of the branch of the cell in the higher areawhich receives input from the two cells active at times 1 and 2 in theprimary area. The black circles indicate newly strengthened synapses.Now, when either cell in the primary area which had been active fires,they will both trigger the same cell to fire in the higher area. In thisway, a shifting sequence of patterns of input become associated with aconstant pattern of activity, the sought-after invariant encoding of theobject, in the higher visual area.

Other features can include formation of a simulated system,demonstrating the performance of this architecture and quantification ofthe time required to recognize an object. In one implementation of asimulation system, there are four areas, each a cortical sheet of 16×16columns of neurons. Each column contacts a pyramidal neuron and aninterneuron. Thus, the simulation entails 2048 individual cells. As inthe mammalian cortex, forward connections from area to area are roughlytopographic, while feedback projections from higher to lower areas havemore widely distributed axonal projections.

The simulation system incorporates the principal neuronal elements. Theindividual neuronal units are not logistic functions or even singlecompartment integrate and fire units. Rather, each simulated neuronincorporates a dendritic tree modeled with compartment model accuracy.In addition, the dendritic membrane is endowed with active electriccurrents, as is the case in biological pyramidal cells. Thesecomplexities of pyramidal neurons are central to their integrative, andprovide a clear advance over prior work; neuronal elements of thisrealism are not used in any extant object recognition system of whichthe author is aware. The power of an electrically active dendritic treeis in allowing local nonlinear integration of input signal patterns inquasi-independent branches. This is a predicted property of realneurons, which has been recently confirmed experimentally. It appearsthat local nonlinear integration of the feedforward synaptic input inthe electrically active branches of dendritic trees is pivotal to enablethe selectivity required for the ability to simultaneously store anddiscriminate a large number of partially overlapping linearlyinseparable objects.

The simulation system incorporates local interneurons. A very commonelement in most pattern recognition models of any type is the inclusionof local lateral inhibition to sharpen representations at eachsucceeding cortical level. Neurons may be modeled as multicompartmentneurons with active dendrites, and connections to their dendriticcompartments may be incorporated. They in turn contact the dendrites andcell body of pyramidal cells within a radius. These units are encoded inthe simulation, and the parameters of their connectivity strength,radius and density is subject to variation to tune the performance ofthe simulated system.

The properties of the synaptic connections between cortical cells arecomplex, stochastic, labile and dynamic. Thus, it is known thatindividual connections between cells of different times have differenttemporal properties, some weakening and others strengthening withrepeated input of a given frequency. It is through these properties thatreal biological synapses may be related to their function withincircuits, and the simultation incorporates realistic properties into thesynaptic connections between the two cell types. In addition, it hasbeen noted that the temporal integration across images which is theheart of the mechanism by which the connections which implementinvariant object recognition self organizes afforded is the long opentime of the NMDA receptor. This receptor, which along with the AMPAmediates much of the excitatory transmission in the cortex, has theseremarkable properties: 1) it remains open for a rather long while (some75 msec) on the timescale of the circuitry (integration in 5-15 msec fora single neuron input/output); 2) it is gated by voltage excitationoccurring at any time after its activation within the 75 msec window;and 3) when current flows through the NMDA receptor, synapse change isinduced. The time window allows features encoding successive view ofobjects in a lower area to be jointly wired to the same cell in a higherarea. This property of cortical synapses will be incorporated into thesynapse in the simulation.

The simulation includes development of a virtual environment and a classof visual objects which can move within that environment, allowing fordilation (as when an object is approached), rotation, and translation. Avirtual visual environment allows a large set of simulated objects todrift across the visual field. As with images of objects in the externalworld as they (or the viewer) move, these simulated images will drift,dilate, and rotate as they pass through the simulated visual field. Atest set of objects will be developed, and an automatic encoding of edgedetectors will be embedded in the first cortical area.

With the simulation constructed in all its elements, and the virtualvisual world programmed, the system may be initialized with small randomconnection weights and then exposed to a library of visual objects. Aseach moves through the visual field in the manner described above,synapses will change strength through a process gated by current throughthe NMDA receptor. The objects will be presented and represented in manydifferent starting and ending positions, so that the system will beexposed to objects in many different random trajectories. During thisvisual experience phase, any synapse modifications will be ongoing, andit is in this sense and during this time the wiring of the neuralcircuitry will self organize. A measure of system performance will bedeveloped to guide parameter changes. Optimal performance will beachieved when each of the set of objects to which the system is exposedtriggers in the higher cortical area a unique distributed pattern which,while different for each object, is unchanging for a given object as itmoves through the visual field, rotates, and dilates in scale.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made without departingfrom the spirit and scope of the claims. For example, while thetechniques have been discussed in terms of visual object recognition,the techniques may be applied in other settings where a temporalsequence of patterns all represent the same object in an abstract sense.Stated another way, the techniques may be used to recode a sequence ofpatterns into a constant item.

What is claimed is:
 1. An object recognition comprising: means forreceiving images; and simulated neural circuitry for recognizing objectsin received images, the simulated neural circuitry comprising ahierarchy of areas made up of neuronal elements, with each neuronalelement comprising a tree of one or more branches, with each of the oneor more branches being connected to receive inputs from multiple otherneuronal elements, wherein the simulated neural circuitry is configuredto: during a training process in which sequences of images representingobjects moving through a visual field are exposed to the neural circuit,establish connectivity of the simulated neural circuitry using thesequences of images such that, after the connectivity is established, animage of each object, positioned at any location in that visual field,activates an invariant pattern of activity representing that object inoutputs of a highest area of the simulated neural circuitry, and afterthe training process, recognize an object in a received image based onan image of the object activating the invariant pattern of activityrepresenting that object in the outputs of the highest area of thesimulated neural circuitry, wherein establishing the connectivity duringthe training process comprises, when images of the object presentedwithin a certain window in time trigger inputs to a branch and activatethe branch, connection between those temporally correlated inputs andthe branch are strengthened, such that in each successively higher areaof the hierarchy the image triggers an increasingly invariant pattern ofactivity.
 2. The system of claim 1, wherein establishing theconnectivity of the simulated neural circuitry comprises: initializingconnections between elements of the neural circuitry; and establishingan initial encoding of a visual image in a pattern of activity ofoutputs of neuronal elements of a lowest area of the simulated neuralcircuitry.
 3. The system of claim 1, wherein the images representmovement of the objects between different starting and ending positions.4. The system of claim 1, wherein the images represent rotation of theobjects.
 5. The system of claim 1, wherein the images represent dilationof the objects.
 6. The system of claim 1, wherein the simulated neuralcircuitry includes simulated neuronal elements with a tree structure forreceipt of input, with each branch entailing local nonlinear integrativeproperties.
 7. The system of claim 1, wherein the simulated neuralcircuitry functions as a self-organizing content addressable memory. 8.The system of claim 1, wherein neuronal elements of the simulated neuralcircuitry are represented as including multiple branches and areconfigured such that a neuronal element is activated when a particularbranch receives a combination of inputs associated with that branch. 9.The system of claim 1, wherein the simulated neural circuitry includesmultiple areas, each of which includes multiple neuronal elements. 10.The system of claim 9, wherein the areas are arranged in a series from alowest area to a highest are and feedforward is provided from outputs ofthe neuronal elements of one area to inputs of neuronal elements of ahigher area.
 11. The system of claim 10, wherein the simulated neuronalcircuitry further comprises feedback from an area to a lower area. 12.The system of claim 1, wherein the dendritic tree is simulated toinclude a dendritic membrane with active electric currents.